5 papers
Stability of Ginzburg-Landau pulses via Fredholm determinants of Birman-Schwinger operators
Erika Gallo, John Zweck, Yuri Latushkin
We introduce a numerical method to determine the stability of stationary pulse solutions of the complex Ginzburg-Landau equation. The method involves the computation of the point s…
A generalized reduction scheme for the Stochastic Weighted Particle Method
Matthew Goeckner, Donovan Harcey, Rainier Q Pederson +2
The Stochastic Weighted Particle Method (SWPM) of Rjasanow and Wagner is a generalization of the Direct Simulation Monte Carlo method for computing the probability density function…
Floquet stability of periodically stationary pulses in a short-pulse fiber laser
Vrushaly Shinglot, John Zweck
The quantitative modeling and design of modern short-pulse fiber lasers cannot be performed with averaged models because of large variations in the pulse parameters within each rou…
Numerical Fredholm determinants for matrix-valued kernels on the real line
Erika Gallo, John Zweck, Yuri Latushkin
We analyze a numerical method for computing Fredholm determinants of trace class and Hilbert Schmidt integral operators defined in terms of matrix-valued kernels on the entire real…
A regularity condition under which integral operators with operator-valued kernels are trace class
John Zweck, Yuri Latushkin, Erika Gallo
We study integral operators on the space of square-integrable functions from a compact set, , to a separable Hilbert space, . The kernel of such an operator takes values in t…